Talk:Poynting vector

Magnetic field naming
This page had the naming of the B and H field wrong in a couple locations. I changed them so that they are consistent with both the rest of the page and the magnetic field page. Hopefully this will reduce confusion of their naming in the future.

Nice work on coax
Commendable work. For an extra flourish, you could assume the load is space cloth with a resistivity of $$ \frac {377} {\sqrt{\epsilon_r}} $$ Ω/□ and show that the power dissipated in each $$ d \rho d \theta $$ is the same as predicted by the Poynting vector. Constant314 (talk) 00:21, 24 November 2021 (UTC)

Nice work indeed. But I think there is no need to mention permittivity and permeability of the materials - they influence nothing (and don't appear in any formula used). Evgeny (talk) 17:09, 24 November 2021 (UTC)
 * Yes, I would just assume vacuum for that discussion. Constant314 (talk) 19:25, 24 November 2021 (UTC)


 * You're right, they don't appear in relation to the main form (ExH) but are still hidden in the definitions of H and E relative to "free" currents and charges. And also (more on this later) there is an entire section on the ExB form which goes so far as to call it the general expression of the Poynting vector! And also a mention (needed?) of the constitutive relations between EDBH under totally unrealistic (or just for low frequencies) conditions (I take non-dispersive to mean "instantaneous"). So it's already mentioned, and hidden, but yes, needn't muddy the text where it can be ignored. I should mention I created the figure before writing the text at which point I realized that epsilon of the dielectric pointed to in the figure had no place in the explanation and proof I wrote up.


 * This also touches on Constant314's mention of "space cloth" termination, and I think I understand what he had in mind in reference to waves along a transmission line, but which he didn't fully think through in the present context. Nor would I have seen this exactly before writing the analysis and let me confess that just because I'm writing about a subject doesn't mean that I jumped into this knowing everything about it just needing to transfer my knowledge to paper. Although I always approach editing a Wikipedia page thinking that I'm going to (and hopefully do!) help educate the next 10,000 readers of that article, especially with a subject like this I am also learning at the same time (and even if not learning something new, at least increasing my familiarity with the subject and writing down equations I might not have looked at for many many years).


 * But what I realized quickly when writing this, is after I limited the analysis (for AC signals at frequency f) to instants << 1/f and lengths of coax << λ=c/f, the concept of a transmission line's characteristic impedance fades into nothingness. Everything you see, applying to some instant, is in terms of the instantaneous V and I with total disregard to how these change in time either individually or with respect to each other, or in space as you go along the transmission line not <<λ. Indeed it works at DC (like the figure it replaced with the battery). It is only an analysis which DOES consider full wave periods and wavelengths when you can talk about "reflected power", standing waves, propagation constants, and characteristic impedance. These DO change depending on epsilon (and mu) but the validity of the Poynting vector can be easily ignored under the above stated restrictions. (I hope I gave you something to think about. I have!)


 * Page still needs a lot of work to flow well, not to mention completeness and (in a couple cases) accuracy, but I tried to put the more important and solid subtopics toward the top. Interferometrist (talk) 19:53, 24 November 2021 (UTC)
 * Yes, AC makes everything more complicated. But all my comments/concerns so far were strictly with DC in mind. For AC, and even more so for pulsed power, permittivity is very important. Maybe the title of the example section should mention DC? Evgeny (talk) 20:58, 24 November 2021 (UTC)
 * Look, you're thinking in electronic terms: that a capacitor in a DC circuit doesn't change anything in the steady-state. But for the Poynting vector even in DC it makes a difference if you use the DxB (or DxH) form (as we don't, but the idea is still out there). The 4 possible forms are a big complication I'd rather ignore, but can't really. My eyes are tired, but could someone else look at the ExB section? It seems wrong. I looked at a paper long ago which goes through all 4 forms and says exactly what each is good for and more importantly how the energy density & dissipation are defined in each case -- not very interesting for me right now but it's within the subject matter of this page. Interferometrist (talk) 21:37, 24 November 2021 (UTC)
 * My understanding is ExH is the right form. If you take D instead of E and repeat the same calculations, you'll end up with a bogus extra energy. Also, I don't think B vs H would make any difference here anyway (unless you mean that the dielectric has non-trivial magnetic permeability). The electric field inside the conductors is zero, so is the Poynting vector... Evgeny (talk) 22:04, 24 November 2021 (UTC)


 * Oh, I almost forgot to mention my main accomplishment: ending the bickering on the talk page ;-) Interferometrist (talk) 19:57, 24 November 2021 (UTC)
 * I never felt like this discussion was bickering. It might have been tedious.  That tends to happen when the participants have different sleep cycles.  I regard it as a healthy, productive, respectful discussion that led to an improvement in the article.  Every comment whether incorporated into the article or rejected helped to lead to a better article.Constant314 (talk) 14:58, 25 November 2021 (UTC)


 * Sure, sure, I wasn't being totally serious! Indeed the discussions are generally helpful not only for the original purpose of agreeing on the wording of the encyclopedia but also is educational or at least thought-provoking for the editors, whether or not that gets reflected in the article seen by the public. I guess by "bickering" I was more thinking of discussions which degenerate into people repeating the same points without converging, or disputing the philosophical meaning of a scientific principle or equation without being able to identify an experiment that would settle it. I guess I might have been thinking more of the Loop antenna page which I will look at again sometime soon after I've completely forgotten what we were arguing about (and fortunately I have a short memory ;-) Interferometrist (talk) 18:39, 25 November 2021 (UTC)

Termination and space cloth
I don’t think that I have ever been guilty of thinking something through entirely. However, I believe my suggestion about space cloth is spot on, except for the incorrect subscript on the permittivity. When a lossless parallel transmission line is terminated by space cloth, it will be terminated by its characteristic impedance at all frequencies including DC. That means that there can be no reflection which means that the PV must be absorbed entirely, with none reflected of allowed to pass through. The energy absorbed when computed by the PV times the area of each ρdρdθ element must be the same when computed by the product of the voltage drop across the element and the current through the element. This works, in part, because once you specify the termination, you establish a relationship between V and I.Constant314 (talk) 15:13, 25 November 2021 (UTC)
 * Well I understand what you have in mind and we've both worked on articles where wave termination by space cloth (or just a resistor for a cable) has relevance. But no, I don't think you thought through the difference between those topics and the issues involved here which concern the local continuity of energy flow on arbitrarily small time and distance scales. That is why the example with coax involved simply a single voltage and current over a tiny time interval and tiny length of coax without any specification of the frequency of the oscillation (including DC) or wavelength (what's happening further down the cable). On that scale, the "wave" picture (which does depend on frequency, wavelength, and propagation velocity) loses its meaning and we are left with E field/voltage and H field/current. There is NO given relationship between V and I implied; these are independent. Sure, you want to and can resolve these into the sum of a forward and backward propagating wave, since that's the way coax is normally used and is evident in standing waves when you look further down the cable or in a ratio and phase between V and I when you look forward in time. And I believe the power of those waves are required if you think you need to express the energy in terms of photons traveling in both directions, but of course ALL the articles in electromagnetics are within the realm of classical physics and photons (however you conceive them, I could tell you how I feel about the subject but then I'd be defying my own dictum in the above paragraph!) do not enter into the picture. So discussing waves (in terms of V and I) along the coax is an unneeded and distracting complication for a problem concisely specified by V and I applying to a small space and time interval. Yes you could put space cloth, or a resistor, of ANY value at the right side of the coax segment and all you have done now is constrained V and I to that resistance but there is nothing in the analysis that ties that space cloth or resistor to what you would normally compute as the characteristic impedance of the cable or dielectric medium. At DC (where the coax analysis is equally valid, as the previous figure had specified) the constraints I mentioned on the allowed spatial and temporal extent of the analysis disappear and the concept of characteristic impedance becomes irrelevant, you can transfer power using arbitrary I and V. (And in case you're thinking of the surge response, note that a step function is NOT DC, it's a mixture of frequencies as you well know). Agree? Interferometrist (talk) 18:47, 25 November 2021 (UTC)
 * I agree with most of that. I am suggesting adding a special case to  your fine work and that is the case where the load is space cloth.  The nice thing in this special case is that your expressions for E, H, and PV apply all the way to the load since a lossless parallel transmission line terminated with space cloth is the same as the same transmission line terminated with and infinite line of the same type.  Part of the old diagram that was lost showed the PV being absorbed by the load.  This special case would bring that back.  It also nicely ties classical EM to circuit theory by showing that the power distribution computed from PV is the same as computed by circuit theory, in this special case.  Of course, that should be true in all cases, but in most cases, calculating the PV in the vicinity of the load is intractable.  Constant314 (talk) 19:53, 25 November 2021 (UTC)
 * Well I haven't thought this through. My initial reaction, identical to what I was saying earlier, is that this would only make a difference if you were to turn the problem into a longer length of coax driven with AC over more than a tiny fraction of a wavelength. Now I can see how space cloth would absorb a plane wave in free space of any frequency, but the wave inside the coax is planer but not (part of) a plane wave since its amplitude varies over the cross section. But indeed its wave impedance E/H matches space cloth at every point in the cross section. I'm trying to see (in the DC case, for instance) what difference it would make if you used space cloth that did not match that impedance. Maybe it'll come to me in the shower or something... Interferometrist (talk) 21:15, 25 November 2021 (UTC)
 * Actually, space cloth will not absorb a wave in free space. However, when you use it to terminate a parallel conductor lossless transmission line (TEM mode) it will be a perfect termination.  If you use space cloth of a different resistivity in the DC case, I'll have to think about that.  Crawford in Waves, Berkeley Physics Course Volume 3, around p. 230 discusses why space cloth will not absorb a wave in free space. Constant314 (talk) 21:25, 25 November 2021 (UTC)
 * So you're saying that "space cloth" is just a clever way of finding the correct terminating resistor for a conductor geometry when you know the wave impedance inside/around the conductors is eta_0/sqrt(eps_r)? A different way of computing a cable's characteristic impedance? But geometrically more symmetrical than a single resistor from the center conductor to an arbitrary point on the shield, so it would make a nicer figure? Is what you think would be nice to show is the Poynting vectors at each point impinging on the space cloth and ending there? Interferometrist (talk) 21:47, 25 November 2021 (UTC)
 * Yes, to all of that. The space cloth idealization reduces the calculation of  characteristic impedance to the calculation of the resistance of a two-dimensional surface, which is easily solved numerically by the Relaxation (iterative method).  But the reason I am suggesting it as a special case is that it would be easy to draw an accurate depiction. Constant314 (talk) 22:00, 25 November 2021 (UTC)

New graph
The new graph is good but I think I improved the caption. I also moved it up and made it smaller so the text could wrap around it. But by doing so it's harder to read the text ON the graph, particularly the legend. If its easy (I'm imagining 2 minutes, but if 2 hours then forget it!) could you change the font it uses? It would probably be enough to just make it bold, though I also find sans-serif fonts better when symbols/equations are involved (but perhaps that's just me). Or you could also remove the legend and mention the colors in the caption (only adding 3 words). Interferometrist (talk) 21:25, 24 November 2021 (UTC)
 * I increased the font size. Evgeny (talk) 21:44, 24 November 2021 (UTC)
 * And also changed to Helvetica − somehow missed it earlier. Evgeny (talk) 08:57, 25 November 2021 (UTC)
 * Great graph. Constant314 (talk) 14:35, 25 November 2021 (UTC)

Right-hand rule?
It would be useful if somebody would add a line of text describing the application of the right (if that's correct) -hand rule to the E, H and S vectors. This would fit nicely in the "Definition" section 90.241.239.175 (talk) 14:25, 21 March 2023 (UTC)